Video: AQA GCSE Mathematics Foundation Tier Pack 4 • Paper 1 • Question 24

Which of these has the greatest value? Circle your answer. [A] 3.8 × 10³ [B] 37199 [C] 3.72 × 10⁴ [D] 37.19 × 10³

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Video Transcript

Which of these has the greatest value? Circle your answer. Is it 3.8 multiplied by 10 to the power of three, 37199, 3.72 multiplied by 10 to the power of four, or 37.19 multiplied by 10 to the power of three?

In order to compare these four numbers, we need to write the first, third, and fourth as an ordinary number. 10 to the power of three or 10 cubed is the same as 10 multiplied by 10 multiplied by 10. This is equal to 1000. This means that 3.8 multiplied by 10 to the power of three is equal to 3.8 multiplied by 1000. Multiplying any number by 1000 moves all the digits three places to the left. The three moves from the units to the thousands. And the eight moves from the tenths to the hundreds. Therefore, 3.8 multiplied by 1000 is 3800.

As 10 to the power of three was equal to 1000, 10 to the power of four is equal to 10000. Therefore, 3.72 multiplied by 10 to the power of four is the same as 3.72 multiplied by 10000. This time, we need to move all the digits four places to the left as there are four zeros. This gives us an answer of 37200. The final option, 37.19 multiplied by 10 to the power of three is the same as 37.19 multiplied by 1000. This time, we need to move the digits three places to the left. Moving digits three places to the left gives us an answer of 37190.

We now need to compare the four numbers, 3800, 37199, 37200, and 37190. The easiest way to do this is to line them up underneath each other using place value columns. As the first number 3800 has no digit in the ten thousands column, this cannot be the greatest value. The other three numbers all have the digit three in the ten thousands column and seven in the thousands column. This means that we need to compare the digits in the hundreds column. Two of these digits are one. And one of them is two. As two is greater than one, this will be the greatest number. The largest of our four numbers in the place value table is 37200. As this corresponded to 3.72 multiplied by 10 to the power of four, then this is the greatest value.

3.72 multiplied by 10 to the power of four is greater than 3.8 multiplied by 10 to the power of three, 37199, and 37.19 multiplied by 10 to the power of three.

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